Converse theorems of summability for Dirichlet’s series

Szász, Otto

doi:10.1090/S0002-9947-1936-1501837-3

Converse theorems of summability for Dirichlet's series

Author: Otto Szász
Journal: Trans. Amer. Math. Soc. 39 (1936), 117-130
MSC: Primary 40A30
DOI: https://doi.org/10.1090/S0002-9947-1936-1501837-3
MathSciNet review: 1501837
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[1] K. Ananda-Rau, On the converse of Abel's theorem, Journal of the London Mathematical Society, vol. 3 (1928), pp. 200-205.
[2] -An example in the theory of summation of series by Riesz's typical means, Proceedings of the London Mathematical Society, (2), vol. 30 (1930), pp. 367-378.
[3] -On a Tauberian theorem concerning Dirichlet's series with positive coefficients, Quarterly Journal of Mathematics, (Oxford series), vol. 2 (1931), pp. 310-312.
[4] H. G. Hardy and J. E. Littlewood, A further note on the converse of Abel's theorem, Proceedings of the London Mathematical Society, (2), vol. 25 (1926), pp. 219-236.
[5] V. Ganapathy Iyer, Tauberian and summability theorems on Dirichlet’s series, Ann. of Math. (2) 36 (1935), no. 1, 100–116. MR 1503211, https://doi.org/10.2307/1968667
[6] E. Landau, Über einen Satz des Herrn Littlewood, Rendiconti del Circolo Matematico di Palermo, vol. 35 (1913), pp. 265-276.
[7] J. E. Littlewood, The converse of Abel's theorem on power series, Proceedings of the London Mathematical Society, (2), vol. 9 (1910), pp. 434-448.
[8] L. Neder, Über Taubersche Bedingungen, Proceedings of the London Mathematical Society, (2), vol. 23 (1925), pp. 172-184.
[9] O. Szász, Über Dirichletsche Reihen an der Konvergenzgrenze, Atti del Congresso Internazionale dei Matematici, Bologna, vol. III, pp. 269-276, 1928.
[10] -Verallgemeinerung und neuer Beweis einiger Sätze Tauberscher Art, Münchner Sitzungsberichte, 1929, pp. 325-340.
[11] Otto Szász, Generalization of two theorems of Hardy and Littlewood on power series, Duke Math. J. 1 (1935), no. 1, 105–111. MR 1545869, https://doi.org/10.1215/S0012-7094-35-00111-9